SOLUTION: How do I simplify the following expressions? 1. x^2-2x-15/x^2-4x-5 2. 4x^2y^3/x^5y^6 * xy/20x^3 3. x^2-7x-8/3x^2-24x * 4x^3/x^2-1 4. (x+5) * x^2-36/x^2+11x+30 Pl

Question 181445: How do I simplify the following expressions?
1. x^2-2x-15/x^2-4x-5
2. 4x^2y^3/x^5y^6 * xy/20x^3
3. x^2-7x-8/3x^2-24x * 4x^3/x^2-1
4. (x+5) * x^2-36/x^2+11x+30

Please help, thanks.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
How do I simplify the following expressions?
1. x^2-2x-15/x^2-4x-5
[(x-5)(x+3)] / [(x-5)(x+1)]
--------------------------------

2. 4x^2y^3/x^5y^6 * xy/20x^3
Reduce each fraction where you can to get:
[(4/x^3y^3)] * [y/20x^2]
Cancel any factors common to a numerator and a denominator:
= [1/x^3y^2] * [1/5x^2]
= [1/(x^5y^2)]
====================
3. x^2-7x-8/3x^2-24x * 4x^3/x^2-1
= [(x-8)(x+1) / 3x(x-8)] * [4x^3/(x-1)(x+1)]
Cancel any factors common to a numerator and a denominator to get:
= [1/3] * [ 4x^2/(x-1)]
= [4x^2/3(x-1)]
======================
4. (x+5) * x^2-36/x^2+11x+30
= (x+5) * [(x-6)(x+6)/(x+6)(x+5)]
Cancel any factor that is common to a numerator and a denominator.
= (1) * (x-6)
= x-6
============
Cheers,
Stan H.

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